A rotary steerable system can be implemented in directional drilling to gradually steer a drill bit attached to a drill string in a desired direction. In directional and horizontal drilling, real-time knowledge of angular orientation of a fixed reference point (called “tool face”) on a circumference of the drill string in relation to a reference point on the wellbore can be important. In a rotary steerable system, for example, knowledge of the tool face can be used to actuate the system in a particular angular location. The reference point can be, for example, magnetic north in a vertical wellbore or the high side of the wellbore in an inclined wellbore. Thus, guiding a drill string using a rotary steerable system can require that the tool face be fixed (i.e., stationary).
Tool face can be measured in terms of magnetic tool face (MTF) or gravity tool face (GTF) or both. Tool face can be determined using GTF by measuring components of gravity in three Cartesian coordinate directions (X, Y and Z directions), which can be converted into inclination. But, the drilling conditions can cause the geo-stationary reference point to which the accelerometers are mounted to become non-stationary, which, in turn, can negatively affect tool face determination. For example, vibrations generated during rotary drilling using rotary steerable systems can distort acceleration due to gravity. The distortion can make the measurement of instantaneous values of acceleration due to gravity in the X, Y and Z directions difficult. MTF uses the earth's magnetic field to obtain the tool face with reference to true magnetic north. When rotary systems drill at speeds exceeding 300 rpm and where measurement is needed every millisecond, measuring the magnetic fields with sufficient accuracy can be burdensome to downhole computer and microprocessor systems. In some situations, the MTF may also need to be converted to GTF to get inclinations, which can require solving complex equations. Doing so can also be burdensome on the downhole computer and microprocessor systems.
Like reference symbols in the various drawings indicate like elements.